## Other odd sided dice: Asymmetric bipyramid

This is a quick prototype I did while sorting out how to do bipyramids on my milling machine. On the next version, recesses will be made (more like the carbon fiber D3) to stamp the numbers in the correct position.

On the first photo, you can count 8 sides, while on the other, there are 7, making this a D15 ^^

Extensive testing will be made before any is put for sale. Any mathematician advise will be welcome ^^

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Odd but original!!!

HeaDLesS - 07/29/2010 at 3:10 pm |

Cooool! Thanks for giving it a try!

johnkzin - 07/29/2010 at 3:28 pm |

I’ve been wanting one of those for years!!

I’m excitedโNow, If I could just find a job, so that I could have some discresionary income again.

Unemployment is not fun.

UTSquishy - 07/29/2010 at 5:54 pm |

Ooooh, nice! ๐

Mathematically, I’m not sure how the probability will work out as the outcomes aren’t equally likely any more. Assuming the two “sides” have the same probability, each of the numbers on the seven sided side is more likely than the ones on the eight sided side – 1/14 to 1/16 respectively, not 1/15 each as it should be.

However, as it’s irregular (or semi-regular) it’s pretty likely that the centre of mass is off-centre anyway… if you could shift it toward the seven sided side so that the eight sided was more likely to come up, you might be able to balance the probabilities out. So you’d need the eight sided side to come up 8/15 of the time, and the seven sided to come up 7/15 of the time…

Do I win a geek point??

Tom - 07/29/2010 at 8:06 pm |

1 geek point for you ๐

First test will involve making a bigger die (this has 10 mm diameter) and then painting it one side black, other side white. Then I’ll throw it tons of times, to see if it is balanced (same number of white faces than black faces). How many throws do you recommend to do? 1000? (no kidding, I’m just asking)

Also, thinking about it, IF both sides have the same probability (remember: test to be done) does it really matter that each number on a face is 1/14 or 1/16? Once the die has chosen to land on a given side…it will “select” one from 7 or one from 8…but one does not affect the other, since they are on different sides…

dicecreator - 07/29/2010 at 8:47 pm |

Hurrah!

No idea about the number of throws – but more is better. Keep working out your relative frequencies every …say 50 throws? When the numbers smooth out you should be able to see if it’s tending towards 0.5 or not – and then you can stop! ๐

The 1/14 and 1/16 are the overall probabilities, sorry. You multiply the probabilities for the side and face together: 1/2 x 1/7 = 1/14 for any face on one side, and 1/2 x 1/8 = 1/16 for any face on the other side.

IF you could make it land on each side in the right 7/15 to 8/15 ratio, you’d have the first side at 7/15 x 1/7 = 7/105, or 1/15 and the other at 8/15 x 1/8 = 8/120, or 1/15 as well.

If it was balanced so that the black and white sides were equally likely, then you wouldn’t get a fair die. Thinking of it as two pyramids “glued” base to base, you would have to make the octagonal-based one slightly taller to shift the centre of mass that way… to make it land on that side 8/15 of the time, which is only just over half anyway… assuming the areas of the bases are the same, the octagonal pyramid needs to be 8/7 of the height of the heptagonal one, then it should work.

Should! lol

Good luck, amazing idea and it would be great to see it work. ๐

Tom - 07/30/2010 at 4:16 pm